Long B. Nguyen, Hyunseong Linus Kim, Dat Thanh Le, Thomas Ersevim, Sai Pavan Chitta, Trevor Chistolini, Christian Jünger, W. Clarke Smith, Thomas M. Stace, Jens Koch, David Santiago, Irfan A. Siddiqi
Decoherence errors arising from noisy environments remain a central obstacle to progress in quantum computation and information processing. Quantum error correction (QEC) based on the Gottesman-Kitaev-Preskill (GKP) protocol offers a powerful strategy to overcome this challenge, with successful demonstrations in trapped ions, superconducting circuits, and photonics. Beyond active QEC, a compelling alternative is to engineer Hamiltonians that intrinsically enforce stabilizers, offering passive protection akin to topological models. Inspired by the GKP encoding scheme, we implement a superconducting qubit whose eigenstates form protected grid states - long envisioned but not previously realized - by integrating an effective Cooper-quartet junction with a quantum phase-slip element embedded in a high-impedance circuit. Spectroscopic measurements reveal pairs of degenerate states separated by large energy gaps, in excellent agreement with theoretical predictions. Remarkably, our observations indicate that the circuit tolerates small disorders and gains robustness against environmental noise as its parameters approach the ideal regime, establishing a new framework for exploring superconducting hardware. These findings also showcase the versatility of the superconducting circuit toolbox, setting the stage for future exploration of advanced solid-state devices with emergent properties.
Decoherence errors arising from noisy environments remain a central obstacle to progress in quantum computation and information processing. Quantum error correction (QEC) based on the Gottesman-Kitaev-Preskill (GKP) protocol offers a powerful strategy to overcome this challenge, with successful demonstrations in trapped ions, superconducting circuits, and photonics. Beyond active QEC, a compelling alternative is to engineer Hamiltonians that intrinsically enforce stabilizers, offering passive protection akin to topological models. Inspired by the GKP encoding scheme, we implement a superconducting qubit whose eigenstates form protected grid states - long envisioned but not previously realized - by integrating an effective Cooper-quartet junction with a quantum phase-slip element embedded in a high-impedance circuit. Spectroscopic measurements reveal pairs of degenerate states separated by large energy gaps, in excellent agreement with theoretical predictions. Remarkably, our observations indicate that the circuit tolerates small disorders and gains robustness against environmental noise as its parameters approach the ideal regime, establishing a new framework for exploring superconducting hardware. These findings also showcase the versatility of the superconducting circuit toolbox, setting the stage for future exploration of advanced solid-state devices with emergent properties.
The prospects for a utility-scale, fault-tolerant superconducting quantum computer have grown increasingly promising through demonstrations of quantum advantage and quantum error correction. The next breakthrough will likely be driven by processors at scale, with qubit counts exceeding tens of thousands. Achieving this scale presents a formidable challenge for current architectures, including limitations in chip footprint, cryogenic cooling capacity, and control complexity. One approach to alleviating these constraints is to make each qubit better, thereby reducing the redundancy required for error correction. Protected qubits provide a promising path in this direction by encoding quantum information into a decoherence-free subspace. This can be achieved through Hamiltonian engineering in superconducting circuits, with representative examples including the 0–π qubit, the cos(2φ) qubit, and the GKP qubit. In this thesis, we present the superconducting grid states qubit, or gridium, as a strong candidate for protected qubits. The gridium consists of a Cooper-quartet tunneling element shunted by a quantum phase slip element. We show that the gridium realizes a decoherence-free subspace within a single mode and can achieve strong protection using readily available superconducting circuit elements. We further demonstrate that its key components—Cooper-quartet tunneling and quantum phase slip—can be realized and engineered through appropriate circuit design, as illustrated with a prototype device. By applying Hamiltonian engineering, we construct three gridium devices with varying levels of protection. We show that the measured spectra are consistent with numerical simulations of the theoretical model. From these fits, we extract the corresponding wavefunctions and observe enhanced protection as the number of grids increases. To directly probe this protection, we measure the depolarization times of the devices while dynamically tuning the protection via flux control. Our best device exhibits T1 = 2.4 ms, comparable to state-of-the-art superconducting qubits. The gridium architecture presented in this thesis demonstrates strong potential for realizing fault-tolerant quantum processors based on protected qubits.
Straightforward logical operations contrasting with complex state preparation are the hallmarks of the bosonic encoding proposed by Gottesman, Kitaev, and Preskill (GKP). The recently reported generation and error correction of GKP qubits in trapped ions and superconducting circuits thus holds great promise for the future of quantum computing architectures based on such encoded qubits. However, these experiments rely on error-syndrome detection via an auxiliary physical qubit, whose noise may propagate and corrupt the encoded GKP qubit. We propose a simple module composed of two oscillators and a physical qubit, operated with two experimentally accessible quantum gates and elementary feedback controls to implement an error-corrected GKP qubit protected from such propagating errors. In the idealized setting of periodic GKP states, we develop efficient numerical methods to optimize our protocol parameters and show that errors of the encoded qubit stemming from flips of the physical qubit and diffusion of the oscillators state in phase space may be exponentially suppressed as the noise strength over individual operations is decreased. Our approach circumvents the main roadblock towards fault-tolerant quantum computation with GKP qubits.
Straightforward logical operations contrasting with complex state preparation are the hallmarks of the bosonic encoding proposed by Gottesman, Kitaev and Preskill (GKP). The recently reported generation and error-correction of GKP qubits in trapped ions and superconducting circuits thus holds great promise for the future of quantum computing architectures based on such encoded qubits. However, these experiments rely on error-syndrome detection via an auxiliary physical qubit, whose noise may propagate and corrupt the encoded GKP qubit. We propose a simple module composed of two oscillators and a physical qubit, operated with two experimentally accessible quantum gates and elementary feedback controls to implement an error-corrected GKP qubit protected from such propagating errors. In the idealized setting of periodic GKP states, we develop efficient numerical methods to optimize our protocol parameters and show that errors of the encoded qubit stemming from flips of the physical qubit and diffusion of the oscillators state in phase-space may be exponentially suppressed as the noise strength over individual operations is decreased. Our approach circumvents the main roadblock towards fault-tolerant quantum computation with GKP qubits.
We present a circuit design composed of two Josephson junctions coupled by a nonreciprocal element, the gyrator, whose ground space is doubly degenerate.The ground states are approximate code words of the Gottesman-Kitaev-Preskill code.We determine the low-energy dynamics of the circuit by working out the equivalence of this system to the problem of a single electron in a crystal, confined to a two-dimensional plane, and subjected to a strong, homogeneous magnetic field.We find that the circuit is naturally protected against the common noise channels in superconducting circuits, such as charge and flux noise, implying that it can be used for passive quantum error correction.We also propose realistic design parameters for an experimental realization, and we describe possible protocols to perform logical one-and two-qubit gates, state preparation, and readout.
We propose a novel approach to generate, protect, and control Gottesman-Kitaev-Preskill (GKP) qubits. It employs a microwave frequency comb parametrically modulating a Josephson circuit to enforce a dissipative dynamics of a high-impedance circuit mode, autonomously stabilizing the finite-energy GKP code. The encoded GKP qubit is robustly protected against all dominant decoherence channels plaguing superconducting circuits but quasiparticle poisoning. In particular, noise from ancillary modes leveraged for dissipation engineering does not propagate at the logical level. In a state-of-the-art experimental setup, we estimate that the encoded qubit lifetime could extend 2 orders of magnitude beyond the break-even point, with substantial margin for improvement through progress in fabrication and control electronics. Qubit initialization, readout, and control via Clifford gates can be performed while maintaining the code stabilization, paving the way toward the assembly of GKP qubits in a fault-tolerant quantum computing architecture.
Bosonic quantum error correction encodes a logical qubit in an oscillator, avoiding the hardware overhead of large qubit arrays. Among such encodings, Gottesman-Kitaev-Preskill (GKP) states are paticularly powerful because their phase-space grid structure protects against small displacement errors simultaneously in both conjugate quadratures. Here we provide the first protocol for preparing magnonic GKP states, which involves an ellipsoidal magnetic crystal effectively coupled to a superconducting qubit via a microwave cavity. The geometric anisotropy intrinsically squeezes the magnon mode, while the cavity-mediated qubit control realizes an effective conditional-displacement interaction. We show that two rounds of a conditional-displacement interaction and a qubit projective measurement yield three- and four-component magnonic GKP-like states. We also show how to realize single logical qubit gate operations, such as Pauli, Hadamard and phase gates, completing the logical Pauli basis of the approximate GKP code. Our results establish hybrid magnon-qubit systems as a promising platform for preparing bosonic code states, with applications in magnonic fault-tolerant quantum computation and quantum sensing.